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Solved problems for the chapter:

Doppler Effect of Sound Waves

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Doppler Effect

1. The sound source is stationary, and the observer is moving

2. The sound source is moving, and the observer is stationary

3. Mach cone

4. Forum

↓ Show theory [1] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:doppler_effect_of_sound_waves/4062/

Example 1.

A motorboat travels on water at a speed of 43 km/h. The waves caused by the boat form an angle of 50 degrees. What is the speed of the waves?

Example 2.

A train travels uniformly at a speed of 100 km/h. It emits a tone of 450 Hz with a siren. What frequency is heard by a stationary observer by the rail track before the train reaches him and when the train moves away from him? The speed of sound is 340 m/s.

The car moving at a speed of 80 km/hr, is approaching a stationary siren emitting a tone at a frequency of 500 Hz. What frequency does a passenger in the car hear as it approaches and moves away from the source of the sound? The speed of sound in air is 340 m/s.

At what speed must we approach a stationary sound source in order to hear an octave-higher tone (twice the sound frequency)?

An ambulance with its siren on is approaching a tall building at a speed of 80 km/h. The siren emits a sound with a frequency of 400 Hz. The sound bounces off the building back towards the ambulance. What frequency of the reflected sound does the ambulance driver hear?

Waves with a frequency of 0.1 Hz and a wavelength of 50 m travel at sea level. A motorboat travels at a speed of 10 m/s against the waves. With what frequency do the waves hit the boat? What is the relative speed of the boat with respect to the waves?

A car is traveling at a speed of 36 km/h when an ambulance with its siren on approaches it from behind at a speed of 90 km/h. The siren emits a tone with a frequency of 400 Hz. What frequency does the car driver hear if:

there is no wind?
the wind blows in the direction of travel of both vehicles at a speed of 20 m/s?
both vehicles are stationary and only the wind is blowing?

The speed of sound in the air is 340 m/s.

A car approaches a stationary listener at a speed of 72 km/h and emits a tone of 600 Hz. At the same time, another car moves away from the stationary listener at a speed of 54 km/h and emits a tone of unknown frequency. What is this unknown frequency if the stationary listener hears a tone of the same frequency from both cars? What frequency of the tone is heard by the stationary listener? The speed of sound is in air 340 m/s.

An airplane flies at twice the speed of sound. What is the angle at the top of the Mach cone?

10.

A loudspeaker is attached to a cord 0.6 m long and waved horizontally at a frequency of 2 Hz. The speaker emits a tone with a frequency of 800 Hz. What are the maximum and minimum frequencies heard by a distant stationary listener? The speed of sound is 340 m/s.

11.

The siren of a moving police car emits a sound wave with a frequency of . A stationary observer hears sound of frequency . The speed of sound in the air is . What could be the speed and the direction of movement of the car?

directly away from the observer
directly towards the observer
directly away from the observer
directly towards from the observer

12.

A source of sound waves with constant frequency moves towards a stationary observer. The observer compares the sound waves arriving at the observer’s position with the waves emitted by the source of sound. What is detected by the observer?

no change in frequency of the sound waves
a decreased frequency of the sound waves
no change in wavelength of the sound waves
a decreased wavelength of the sound waves

13.

An observer hears a sound wave emitted from a moving source. The observed frequency is less than the frequency of sound emitted from the source. What could be the reason for this?

The source is moving away from the observer.
The source is moving towards the observer.
The speed of the sound wave in air decreases due to the movement of the source.
The speed of the sound wave in air increases due to the movement of the source.

14.

An ambulance siren emits a sound with a single frequency . The ambulance travels towards, passes close to, and then travels away from a stationary observer. Which statement describes the frequency of the sound detected by the observer as the ambulance passes the observer?

equal to and increasing
less than and constant
equal to and decreasing
greater than and constant

15.

A siren emits sound of frequency . The siren moves at towards an observer who is standing still. The speed of sound in the air is . Which expression would correctly give the frequency heard by the observer?

16.

A source of sound waves is moving at a constant speed directly towards a stationary observer. The sound waves have a speed of and a frequency of . The observer hears sound waves of frequency . What is the speed of the source?

17.

A loudspeaker emits sound of frequency . the loudspeaker is attached to a car that moves with increasing speed directly towards a stationary observer. Which statement describes the frequency of the sound heard by the observer?

a frequency greater than and increasing
a frequency greater than but decreasing
a frequency less than and decreasing
a frequency less than but increasing

18.

A source of sound of frequency of directly approaches a stationary observer. The observer measures the frequency of the received sound to be . The speed of sound in still air is . What is the speed of the source of sound?

19.

An emergency vehicle sounds its siren as it accelerates along a straight road between two points X and Y, as shown in the diagram.

The frequency of the sound emitted by the siren is . A person stands at X and another person stands at Y. What describes the sounds heard by the people at X and at Y as the vehicle accelerates?

	sound heard by person at X	sound heard by person at Y
A	higher than , increasing in frequency	lower than , decreasing in frequency
B	higher than , decreasing in frequency	lower than , increasing in frequency
C	lower than , decreasing in frequency	higher than , increasing in frequency
D	lower than , increasing in frequency	higher than , decreasing in frequency

20.

The horn of a train emits sound of frequency . While the horn is sounding, the train moves directly towards a stationary person. The speed of the train is , where is the speed of sound. The frequency of the sound heard by the person is . What is the ratio ?

21.

A car travels at a constant speed along a straight line PQ. A loudspeaker attached to the car emits sound of constant frequency . A stationary observer is at point O.

What does the observer hear as the car moves from P towards Q?

a frequency less than that decreases as the car moves from P towards Q
a frequency less than that increases as the car moves from P towards Q
a frequency more than that decreases as the car moves from P towards Q
a frequency more than that increases as the car moves from P towards Q

22.

An observer is standing on a railway platform. A train passes the observer at constant speed while emitting sound of constant frequency from its whistle. What does the observer hear?

sound of a decreasing frequency as the train approaches and of an increasing frequency as it moves away
sound of a higher frequency than as the train approaches and of a lower frequency than as the train moves away
sound of a lower frequency than as the train approaches and of a higher frequency than as the train moves away
sound of an increasing frequency as the train approaches and as it moves away

23.

A source X emits a sound wave of constant frequency . The wave is subsequently received at a stationary detector Y. The frequency of the wave that is detected by Y is less than . What could be the reason for this?

Between X and Y, the wave undergoes diffraction.
Between X and Y, the wave undergoes reflection.
X is moving away from Y.
X is moving towards Y.

24.

A vehicle moves with constant velocity along a road directly towards an observer. The observed frequency of the sound from the vehicle changes as the vehicle moves past the observer. Which phenomenon explains the change in frequency?

diffraction
interference
polarisation
the Doppler effect

25.

A jet aircraft travels at a speed of , where is the speed of sound. The aircraft directly approaches a stationary observer. The frequency of sound emitted by the aircraft is . Which frequency does the observer hear?

26.

A car is travelling at a constant velocity directly towards a man standing in the middle of the road. The driver sounds the car’s horn as a warning. The horn emits a sound wave of constant frequency. The frequency of the sound heard by the man is different from the frequency of the sound emitted by the horn. Which statement is correct?

The frequency of the sound emitted by the horn is greater than the frequency of the sound heard by the man.
The frequency of the sound heard by the man depends on the distance between the car and the man.
The sound waves continually accelerate as they move from the horn to the man.
The wavelength of the sound heard by the man is less than the wavelength of the sound emitted by the horn.

27.

A source emits a sound wave of a single frequency. The Doppler effect causes a different frequency of sound to be heard by a stationary observer. What is a requirement for the Doppler effect to occur?

a source that is moving as it produces the sound wave
a source that produces a polarised sound wave
a source that produces a sound wave of changing amplitude
a source that produces a sound wave of changing frequency

28.

A man standing next to a stationary train hears sound of frequency emitted from the train’s horn. The train then moves directly away from the man and sounds its horn when it has a speed of . The speed of sound in the air is . What is the difference in frequency of the sound heard by the man on the two occasions?

29.

The warning signal on an ambulance has a frequency of . The speed of sound is . The ambulance is travelling with a constant velocity of towards an observer. The ambulance passes, and then moves away from the observer with no change in velocity. Which overall change in observed frequency takes place between the times at which the ambulance is a long way behind the observer and when it is a long way in front of the observer?

30.

An ambulance has a siren that emits sound of a constant frequency. The ambulance is moving directly towards a stationary observer. The ambulance decelerates as it is approaching the observer and then accelerates after it has passed the observer. How does the frequency of the sound heard by the observer change as the ambulance is approaching and as it is moving away from the observer?

	approaching observer	moving away from observer
A	decreases	decreases
B	decreases	increases
C	increases	decreases
D	increases	increases